论文标题
统计力学的投影操作员：一种教学方法
Projection operators in statistical mechanics: a pedagogical approach
论文作者
论文摘要
Mori-Zwanzig投影操作员形式主义是非平衡统计力学的中心工具之一，可以通过系统的粗粒程序从微观动力学中得出宏观的运动方程。作为物理研究方法，这一点很重要，并为非平衡传输方程的一般结构和微观派生的一般程序提供了许多见解。因此，它是统计力学基础课程和高级课程的宝贵要素。但是，对此方法的访问介绍 - 特别是在更高级的形式中 - 极为罕见。在本文中，我们对Mori-Zwanzig形式主义进行了简单而系统的介绍，该介绍使学生可以理解当前研究中使用的形式的方法。这包括理论的基本版本和现代版本。此外，我们将形式主义与统计力学和量子力学的更一般方面联系起来。因此，我们解释了如何将这种方法纳入有关统计力学的讲座课程，以此作为对非平衡系统研究的一般介绍的一种方式。还讨论了应用于自旋松弛和动态密度功能理论的应用。
The Mori-Zwanzig projection operator formalism is one of the central tools of nonequilibrium statistical mechanics, allowing to derive macroscopic equations of motion from the microscopic dynamics through a systematic coarse-graining procedure. It is important as a method in physical research and gives many insights into the general structure of nonequilibrium transport equations and the general procedure of microscopic derivations. Therefore, it is a valuable ingredient of basic and advanced courses in statistical mechanics. However, accessible introductions to this method - in particular in its more advanced forms - are extremely rare. In this article, we give a simple and systematic introduction to the Mori-Zwanzig formalism, which allows students to understand the methodology in the form it is used in current research. This includes both basic and modern versions of the theory. Moreover, we relate the formalism to more general aspects of statistical mechanics and quantum mechanics. Thereby, we explain how this method can be incorporated into a lecture course on statistical mechanics as a way to give a general introduction to the study of nonequilibrium systems. Applications, in particular to spin relaxation and dynamical density functional theory, are also discussed.
